Method of grinding the teeth of bevel gears having longitudinally curved teeth

ABSTRACT

The apparatus for grinding rough-cut longitudinally curved gear teeth of a helical bevel gear, comprises two spindles for respectively mounting a tool and a workpiece, and structure for translatably and adjustably arranging at least one spindle of these two spindles. A separate electric motor arranged coaxially with each of the two spindles serves for driving the tool and for driving the workpiece, respectively. The separate electric motors are mutually interconnected by an electric shaft.

CROSS-REFERENCE TO RELATED CASES

This application is a divisional of the commonly assigned, co-pendingU.S. application Ser. No. 06/936,155, filed Dec. 1, 1986 and entitled"METHOD OF GRINDING THE TEETH OF BEVEL GEARS HAVING LONGITUDINALLYCURVED TEETH" now U.S. Pat. No. 4,799,377, granted Jan. 24, 1989.

BACKGROUND OF THE INVENTION

The present invention broadly relates to the fabrication of gear teethon a bevel gear and, more specifically, pertains to a new and improvedmethod, apparatus and tool for finish machining rough machined teeth ofhypoid gears.

Generally speaking, a primary method of the present invention is forgrinding rough-cut longitudinally curved gear teeth of a bevel gearblank by means of a tool driven in rotation about a tool axis andentailing the performance of at least one relative feed motion betweenthe bevel gear blank and the tool.

In other words, the primary method of the present invention is forfabricating gear teeth on a bevel gear and comprises the steps of roughmachining a bevel gear blank with a first axis of rotation and a firstnumber of longitudinally curved teeth each having a longitudinallyconvex tooth flank and each having a longitudinally concave tooth flankwhile leaving a finish machining allowance on each longitudinallyconcave tooth flank and on each longitudinally convex tooth flank andarranging the rough machined bevel gear blank with the first axis ofrotation in a hypoidally displaced relationship to a second axis ofrotation of a rotary form tool.

The tool of the present invention is for grinding rough-cutlongitudinally curved gear teeth of a bevel gear blank and has aconoidally helical form. The tool comprises teeth and each tooth of theteeth has a concave tooth flank and a convex tooth flank.

In other words, the tool of the present invention is a rotary form toolfor finish machining tooth flanks of a first number of longitudinallycurved teeth of a rough machined bevel gear blank for a hypoid gearpair.

The apparatus of the present invention is for grinding rough-cutlongitudinally curved gear teeth of a helical bevel gear.

In other words, the apparatus of the present invention is for finishmachining tooth flanks of a first number of longitudinally curved teethof a rough machined bevel gear blank for a hypoid gear pair by means ofa rotary form tool. The apparatus comprises a first spindle for mountingthe rough machined bevel gear blank and a second spindle for mountingthe rotary form tool. Means are provided for translatably adjusting atleast one spindle of the first spindle and the second spindle.

A further method of the present invention is for using the inventiveapparatus for finish machining tooth flanks of a first number oflongitudinally curved teeth of a rough machined bevel gear blank for ahypoid gear pair by means of a rotary form tool having a second numberof gear teeth and comprises the steps of mounting the rough machinedbevel gear blank in a first spindle of the apparatus, employing as therotary form tool a rotary form tool having a second number of teeth andat least one abrading surface and mounting the rotary form tool in asecond spindle of the apparatus.

A still further method of the present invention is for fabricating atool.

In other words, the still further method of the present invention is forfabricating a rotary form tool having a first axis of rotation and afirst number of gear teeth for finish machining a rough machined helicalbevel gear having a second axis of rotation and a second number oflongitudinally curved teeth. The method comprises the steps of initiallyfabricating a master gear also having the first axis of rotation andcorresponding to the rough machined helical bevel gear to be finishmachined.

Yet a further method of the present invention is for fabricating a tooland comprises the steps of setting up data programs for associatedrough-cut tools and fabricating the rough-cut tools in accordance withthe set-up data programs.

In other words, the yet further method of the present invention is forfabricating a rotary form tool for finish machining a rough machinedbevel gear blank. The method comprises the steps of generating a firstset of dimensional data relating to the configuration of a hypoid gearmaster corresponding to the rough machined bevel gear blank to be finishmachined.

In this specification it is to be understood that a bevel or hypoid gearpair or set or transmission comprises two bevel gears, a so-calledpinion gear (usually smaller and driving) and a so-called crown or ringgear (usually larger and driven).

The manufacturing process for fabricating bevel gears and hypoid geartransmissions to be prefatorily described hereinbelow has proven itsmettle both economically and qualitatively: cutting gear teeth bymilling or shaping; case-hardening; and pairwise lapping. The generalresult is a gear pair comprising a pinion gear and a ring or crown gearwhich must both be marked as members of a matched pair during lapping toensure correct installation later. The inevitable hardening distortionand its ensuing diminution of quality have always caused difficulties.Pairwise lapping reduces or eliminates individual pitch errors forimproving quiet running of the gear set and for finishing the toothflank surfaces, but radial and axial run-out errors persist. If suchradial and axial run-out errors cannot be accommodated or tolerated,more suitable finish machining processes must be employed.

In the mass production of gear transmissions, especially for automobileand heavy vehicle production, cylindrical spur gears are, for instance,rough cut by milling before hardening; usually shaving or hobbing beforehardening; and subsequently hardening. The quality thus attained meetsthe specified requirements, since hardening distortion in cylindricalgears is slight and the involute toothing employed is relativelyinsensitive to radial run-out errors. The arcuately-tooth bevel gearsusually employed in such gear transmissions are fabricated as initiallydescribed and installed in matched pairs without detriment to thequality level of the gear transmission already established by thecylindrical gears. In order to achieve greater economy, it is desired toeliminate the fixed pairing or matching of pinion and crown gear inbevel gear sets, i.e. it is desired to eliminate hardening distortionwhen fine processing or finish machining bevel gear toothing or,respectively, to render distortion retrogressive after hardening.

It has long been known in practice that the toothing of bevel gearsfabricated by rough cutting in the unhardened state according to theindexing method, that is bevel gears having circularly arcuate teeth,can also be ground with dished grinding wheels according to the indexingmethod after case hardening. This method is employed especially whenutmost requirements are demanded of the gear transmission, such as inrotor drives for helicopters. In such applications, the considerablyhigher fabrication costs are of secondary importance. A method forcrowning longitudinally curved teeth of gears fabricated according tothe continuous cutting method is known from the European Patent No.0,022,586, published Jan. 21, 1981, and the cognate U.S. Pat. No.4,467,567, granted Aug. 28, 1984. Both of these fine processing orfinish machining methods are, however, not suited for employment in massproduction, especially in automotive vehicle production, for economicreasons.

A dished or cupped grinding wheel with two conical grinding flanks forgrinding helically or arcuately toothed bevel gears according to theindexing generating method is known from the German Patent No.2,721,164, published Oct. 29, 1981. The grinding flanks confront oneanother and thus form a recessed inner annulus of frustro-conicalcross-section.

A corresponding design of machine is described in the article "Schleifenbogenverzahnter Kegelrader in der Kleinserienfertigung" in the TechnicalJournal Werkstatt und Betrieb, No. 118, October 1985, pages 703 to 705.The introduction to this article indicates that there had heretoforebeen no possibility of grinding the flanks of arcuately toothed bevelgears economically in small lots. The machine described in the articlepermits grinding axially displaced and non-axially displaced bevel gearswith the dished or cupped grinding wheel. The process employs theindexing generating method tooth for tooth. This process is thereforeespecially suited for finishing bevel gears having teeth rough cutaccording to the indexing generating method, i.e. circularly arcuatelyfabricated. Under certain conditions even bevel gears having rough cutteeth with epicycloidal or involute longitudinal flank lines can befinish ground to a circular arc. Should, however, the epicycloidal orinvolute form deviate too greatly from a circular arc, i.e. by more thana permissible amount of grinding allowance, then this method is nolonger utilizable.

A further method for fine processing or finish machining hardenedhelical bevel gears by generating milling is known from thewt-Zeitschrift fur industrielle Fertigung, No. 75, 1985, pages 461 to464. In this method spiral bevel gears rough cut according to thecontinuous generating milling method are finish milled subsequent tocase hardening. The requisite cutting tools substantially correspond tothose employed for milling before hardening, but the cutting edgescomprise hard metal inserts for machining after hardening. The samemachine and procedure can thus be employed for machining both before andafter hardening. The hard metal inserts are preferably mounted ascutting edge strips provided with a coating of polycrystalline cubicboron nitride, also known as CBN or Borazon, on their top rake orcutting faces.

An apparatus for fine processing or finish machining of gears having ashaping or shaving wheel cutter or other gear-shaped tool is known fromthe German Patent No. 1,161,465. In this apparatus the workpiece and thetool roll, i.e. perform generating motions, upon one another in mesh andtheir axes intersect. The workpiece and the tool are each connected by arespective shaft to an associated master gear. That is, the shavingwheel and the associated master gear pair as well as the workpiece gearblank and the associated master pinion pair are each fixed againstrotation on one and the same shaft. This apparatus is, however, onlyemployed for machining straight-toothed gears or helically toothedcylindrical gears. This apparatus is not utilizable for fine processingor finish machining bevel gears having longitudinally curved teeth.

SUMMARY OF THE INVENTION

Therefore, with the foregoing in mind, it is a primary object of thepresent invention to provide a new and improved apparatus for finishmachining bevel gears which does not exhibit the aforementioneddrawbacks and shortcomings of the prior art constructions.

Another and more specific object of the present invention aims atproviding a new and improved apparatus of the previously mentioned typefor grinding bevel gears having longitudinally curved teeth and whichcan be economically employed, especially in both small production runsand large production runs.

Another more specific object of the present invention aims at providinga new and improved apparatus for performing the inventive method.

Yet a further significant object of the present invention aims atproviding a new and improved construction of an apparatus of thecharacter described which is relatively simple in construction anddesign, extremely economical to manufacture, highly reliable inoperation, not readily subject to breakdown and malfunction and requiresa minimum of maintenance and servicing.

Now in order to implement these and still further objects of theinvention, which will become more readily apparent as the descriptionproceeds, the primary method of the present invention, among otherthings, is manifested by the features that it comprises the steps of:employing for the tool a helical bevel gear hypoidally related to therough-cut longitudinally curved gear teeth to be ground of the bevelgear blank; the helical bevel gear having a predetermined number ofteeth; each tooth of the predetermined number of teeth having at leastone tooth flank provided with an abrading surface; arranging the helicalbevel gear in a hypoidally displaced relationship to the rough-cutlongitudinally curved gear teeth to be ground of the bevel gear blank;arranging the helical bevel gear in mesh with the rough-cutlongitudinally curved gear teeth to be ground of the bevel gear blank;positively driving the helical bevel gear and the bevel gear blank in asynchronous relationship at rotary speeds proportional to theirrespective numbers of teeth; selecting the hypoidally displacedrelationship of the helical bevel gear to the rough-cut longitudinallycurved gear teeth to be ground of the bevel gear blank and selecting therotary speeds such that a relative sliding velocity arising therebetweenfalls in the range of conventional or predetermined surface speeds forgrinding; and continuously grinding in a single operation and with theat least one relative feed motion at least a selected set of the set ofall concave tooth flanks and the set of all convex tooth flanks of therough-cut longitudinally curved gear teeth to be ground of the bevelgear blank.

In other words, the primary method of the present invention comprisesthe steps of: employing as the rotary form tool a rotary form toolhaving the configuration of a helical bevel gear with a second number ofgear teeth hypoidally related to the longitudinally curved teeth of therough machined bevel gear blank in correspondence with the hypoidallydisplaced relationship of the first axis of rotation to the second axisof rotation and coated with an abrading medium on at least one toothflank of the second number of gear teeth for removing the finishmachining allowance; meshing the second number of gear teeth with thefirst number of longitudinally curved teeth of the bevel gear blank;rotating the rotary form tool about the second axis of rotation and therough machined bevel gear blank about the first axis of rotationsynchronously in the ratio of the first number of longitudinally curvedteeth of the bevel gear blank to the second number of gear teeth of therotary form tool; selecting the hypoidally displaced relationship of thefirst axis of rotation to the second axis of rotation and a rotary speedof the rotary form tool in relation to the hypoidally displacedrelationship such that a relative sliding velocity arising between thelongitudinally curved teeth and the gear teeth has a value within therange of conventional or predetermined surface speeds for abradingoperations; and continuously abrading in a single operation at least aselected set of the set of all the longitudinal concave tooth flanks andthe set of all the longitudinal convex tooth flanks while performing apredetermined feed motion of the rotary form tool relative to the bevelgear blank.

The tool of the present invention is manifested, among other things, bythe features that at least one abrading surface is provided on at leasta selected tooth flank of at least one concave tooth flank and at leastone convex tooth flank; the bevel gear blank defining a workpiece; andthe tool being designed for cooperation with the bevel gear blank withan axial displacement.

In other words, the rotary form tool of the present invention ismanifested, among other things, by the features that it comprises a toolbody having the configuration of a helical bevel gear with a secondnumber of gear teeth hypoidally related to the first number oflongitudinally curved teeth of the rough machined bevel gear blank; eachtooth of the second number of gear teeth being helically curved andhaving a longitudinally concave tooth flank and a longitudinally convextooth flank; and at least one tooth flank of the longitudinally concavetooth flanks and the longitudinally convex tooth flanks being coatedwith an abrading medium.

The apparatus of the present invention is manifested by the featuresthat it comprises two spindles for mounting a tool and a workpiece,respectively, as well as means for translatably and adjustably arrangingat least one spindle of the two spindles. The apparatus furthercomprises a separate electric motor arranged coaxially with each of thetwo spindles for driving the tool and for driving the workpiece,respectively, and means defining a so-called "electric shaft". Theseparate electric motors are mutually interconnected by the so-called"electric shaft".

In other words, the apparatus of the present invention, among otherthings, is manifested by the features that a first rotary drive means isarranged coaxial to the first spindle for driving the first spindle at afirst speed of rotation and a second rotary drive means distinct fromthe first rotary drive means is arranged coaxial to the second spindlefor driving the second spindle at a second speed of rotation. Theapparatus comprises means interconnecting the first rotary drive meansand the second rotary drive means for synchronizing the first speed ofrotation and the second speed of rotation in a predeterminate ratio.

The further method of the present invention, among other things, ismanifested by the features that it comprises the steps of: adjusting aselected one of the first spindle and the second spindle such that therough machined bevel gear blank and the rotary form tool mesh such thatthe first axis of rotation and the second axis of rotation mutuallydefine a hypoidally displaced relationship in which conjoint rotation ofthe first spindle and the second spindle produces relative slidingbetween tooth flanks of the rough machined bevel gear blank and therotary form tool; selecting the hypoidally displaced relationship and afirst speed of rotation for the second spindle such that the relativesliding has a velocity lying within the range of conventional orpredetermined surface speeds for abrading operations; employing firstrotary drive means to rotate the first spindle at the first speed ofrotation; employing second rotary drive means conjointly with regulationmeans to rotate the second spindle in synchronism with the first spindleat a second speed of rotation related to the first speed of rotation bythe ratio of the first number of longitudinally curved teeth to thesecond number of gear teeth; and effecting a relative feed motionbetween the first spindle and the second spindle.

The still further method of the present invention, among other things,is manifested by the features that it comprises the steps of: (a)coating tooth flanks of gear teeth of one gear of a hypoid geartransmission with an abrading medium; (b) grinding with the coated gearin the guise of a tool rough cut teeth of an associated tool in theguise of a workpiece; and (c) coating the rough cut and now ground teethof the workpiece with an abrading medium.

In other words, the still further method of the present invention, amongother things, is manifested by the features that it comprises the stepsof: coating at least one tooth flank of the master gear with an abradingmedium; fabricating a rough machined working rotary form tool blankhaving the configuration of a helical bevel gear with a first number ofgear teeth hypoidally related to a second number of longitudinallycurved teeth of the rough machined helical bevel gear to be finishmachined; employing the coated master gear as a master rotary form toolto finish machine the rough machined working rotary form tool blank as aworkpiece for producing a finish machined working rotary form tool byarranging the coated master gear with the first axis of rotation in anaxially displaced relationship to the second axis of rotation of therough machined working rotary form tool blank; meshing the first numberof gear teeth with the second number of longitudinally curved teeth;rotating the master rotary form tool about the second axis of rotationand the rough machined working rotary form tool about the first axis ofrotation synchronously in the ratio of the first number of gear teeth tothe second number of longitudinally curved teeth; selecting thehypoidally displaced relationship of the first axis of rotation to thesecond axis of rotation and a rotary speed of the coated master gear inrelation to the hypoidally displaced relationship such that a relativesliding velocity arising between the longitudinally curved teeth and thegear teeth has a value within the range of conventional or predeterminedabrading surface speeds; continuously abrading in a single operation atleast a selected set of the set of all the longitudinally concave toothflanks and the set of all the longitudinally convex tooth flank whileperforming a predetermined feed motion of the coated master gearrelative to the rough machined working rotary form tool blanks; andcoating at least one tooth flank of the finish machined working rotaryform tool with an abrading medium.

A variant embodiment of the still further method of the presentinvention, among other things, is manifested by the features that itcomprises the steps of mounting the rough machined bevel gear blank in afirst spindle of the apparatus; employing as the rotary form tool arotary form tool having a second number of gear teeth and at least oneabrading surface; mounting the rotary form tool in a second spindle ofthe apparatus; adjusting a selected one of the first spindle and thesecond spindle such that the rough machined bevel gear blank and therotary form tool mesh such that the first axis of rotation and thesecond axis of rotation mutually define a hypoidally displacedrelationship in which conjoint rotation of the first spindle and thesecond spindle produces relative sliding between tooth flanks of therough machined bevel gear blank and the rotary form tool; selecting thehypoidally displaced relationship and a first speed of rotation for thesecond spindle such that the relative sliding has a velocity lyingwithin the range of conventional or predetermined surface speeds forabrading operations; employing first rotary drive means to rotate thefirst spindle at the first speed of rotation; employing second rotarydrive mans conjointly with regulation means to rotate the second spindlein synchronism with the first spindle at a second speed of rotationrelated to the first speed of rotation by the ratio of the first numberof longitudinally curved teeth to the second number of gear teeth;effecting a relative feed motion between the first spindle and thesecond spindle; and coating at least one tooth flank of the finishmachined working rotary tool with an abrading medium.

The yet further method of the present invention, among other things, ismanifested by the features that it comprises the steps of: (a)setting-up the data programs for the associated rough-cut tools on thebasis of a stored master gear data program for a hypoid geartransmission; (b) fabricating the rough cut tools in accordance with theset-up data programs; and (c) coating the fabricated tools with anabrading medium.

In other words, the yet further method of the present invention, amongother things, is manifested by the features that it comprises the stepsof: employing the first set of dimensional data for generating a secondset of dimensional data relating to the configuration of a hypoid gearconjugate to the hypoid gear master; fabricating and finish machiningthe rotary form tool according to the second set of dimensional data;and coating at least one tooth flank of the finish machined rotary formtool with an abrading medium.

The advantages attained by the present invention consist in that themethod can be employed independently of the longidutinal form of thebevel gear teeth and independently of the longitudinal tooth profiles,e.g. circular arcs, cyloids or involutes, independently of the presenceor absence of crowning as well as of straight or generated tooth flankprofiles. The method is employed as a continuous grinding process andtherefore favorably influences the economy as well as the quality ofbevel gear transmissions in that the effects of hardening distortion aswell as pitch errors, axial run-out errors and radial run-out errors aresubstantially eliminated and therefore the pairwise identification ormatching of pinion and crown gear as well as their joint storage becomeredundant. Thus, for the first time, accurate mass-produced copies ofmaster gears of a master gear set are possible. A further advantageconsists in that the grinding method can also be employed independentlyof the fabrication of the rough cut bevel gear, whether by forging,rolling, casting, et cetera.

A further advantageous embodiment of the tool consists in that its toothflanks are coated with a thin layer of abrading material, such as cubicboron nitride, for instance Borazon.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will be better undeerstood and objects other than thoseset forth above will become apparent when consideration is given to thefollowing detailed description thereof. such description makes referenceto the annexed drawings wherein throughout the various figures of thedrawings there have been generally used the same reference characters todenote the same or analogous components and wherein:

FIG. 1 shows a cross-section through a pair of bevel gears withintersecting axes;

FIG. 2 shows an arrangement for grinding the crown gear of a bevel gearpair according to FIG. 1;

FIG. 3 schematically shows the axial displacement geometry of the crowngear and the tool;

FIG. 4 schematically shows the mating relationships of developments of aplanar conjugate gear and the tool of FIG. 3 on an enlarged scale;

FIG. 5 shows an arrangement for grinding the pinion gear of the gear setaccording to FIG. 1;

FIG. 6 shows a perspective view of gear teeth for explaining thegrinding direction and relative sliding velocities;

FIG. 7 shows a cross-section through a tool tooth on an enlarged scale;

FIGS. 8a and 8b each show a segment of gear toothing during grindingaccording to a first inventive method on an enlarged scale;

FIG. 9 shows a segment of toothing during grinding according to a secondinventive method on an enlarged scale;

FIG. 10 schematically shows a diagram for determining the surface speedof grinding;

FIG. 11 shows a plan view of the inventive apparatus arranged forgrinding large pinion gears for heavy vehicles;

FIG. 12 shows a plan view analogous to FIG. 11 of the inventiveapparatus arranged for grinding small pinion gears for automobiles;

FIG. 13 shows a plan view analogous to that of FIG. 11 of the inventiveapparatus arranged for grinding large crown gears for heavy vehicles;

FIG. 14 shows a plan view analogous to that of FIG. 11 of the inventiveapparatus arranged for grinding small crown gears for automobiles;

FIG. 15 shows a partial elevation of the inventive apparatus in thedirection of the arrow A in FIG. 11;

FIG. 16 shows a vertical cross-section taken along the line XVI--XVI inFIG. 12;

FIG. 17 shows a cross-section taken along the line XVII--XVII in FIG.16;

FIG. 18 shows a horizontal cross-section taken at the height of the toolspindle in FIG. 11; and

FIG. 19 schematically shows a circuit diagram of a so-called "electricshaft".

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Describing now the drawings, it is to be understood that to simplify theshowing thereof only enough of the structure of the inventive tool andapparatus has been illustrated therein as is needed to enable oneskilled in the art to readily understand the underlying principles andconcepts of this invention. The subsequently described embodimentsillustrated in FIGS. 1 through 10 relate to rough machined bevel gearsto a bevel gear set or bevel gear pair fabricated with a rotating cutterhead in a continuous cutting process. At least, for instance, alongitudinal crowning of the teeth is produced by skewing the cutterhead axis. In principle such rough machined bevel gears can also befabricated by other known manufacturing procedures, possibly resultingin different longitudinal forms of tooth, e.g. circularly arcuate,cycloidal or involute, i.e. the inventive method of finish machining canbe performed independently of the longidutinal form of tooth andindependently of the fabrication of the rough machined blanks for thebevel gears. Merely a different dimensioning of the tool must beemployed in that, according to the selected form of tooth, the principaldimensional data for the tool must be conventionally worked out, butworked out for a tool designed as a component of a gear transmissionwith displaced axes, i.e. a hypoid gear transmission.

Turning now specifically to FIG. 1 of the drawings, it will be seen thata conventional bevel gear pair, also known as bevel gear set or bevelgear transmission, comprises a ring gear or crown gear 1, the largergear of the pair (usually the driven gear), and a pinion gear 2, thesmaller gear of the pair (usually the driving gear), arranged withnon-displaced axes, i.e. with their axes of rotation intersecting at amutual apex 7 of their respective pitch cones. A crown gear axis 3 and apinion gear axis 4 extend, for instance, mutually perpendicular andintersect at the mutual apex 7 of the pitch cones of the bevel gearpair. A toothing 5 of the crown gear 1 may be, for instance, producedsolely by plunge cutting, while a toothing 6 of the pinion gear 2 may beproduced by gear generation, i.e. the teeth of the toothing 5 normallyexhibit straight tooth flanks while those of the toothing 6 exhibitcurved tooth flanks which, although not readily apparent from FIG. 1, iswell-known in the art. For the installation of such a bevel gear set orbevel gear pair comprising a randomly chosen crown gear 1 and a randomlychosen pinion gear 2, both of the bevel gears 1 and 2 are rough machinedin known manner in mass production with a grinding allowance andsubsequently ground.

In FIG. 2, the rough machined crown gear 1 is mounted on a spindle 11 ofa headstock 10 and rotatable about an axis of rotation 9 as a workpiece1a to be ground. The crown gear axis 3 coincides with the axis ofrotation 9 of the spindle 11. The apex 7 of the pitch cone of the crowngear 1 lies on an axis 12 about which a generating drum 13 in agenerating or roll cradle 14 is rotatbly journalled. A pivotingcomponent 15 connected to the generating drum 13 comprises a spindle 17on which a tool or grinding cutter 18 having a tool axis 16 is fastened.The tool 18 is a rotary form tool which is helically conically formedand comprises an abrading surface 19 on its tooth flanks 20. The tool 18is furthermore designed with an axially displaced relationship to theworkpiece 1a, i.e. the axes of rotation of the tool 18 and of theworkpiece 1a do not intersect, and is designed to form conjointlytherewith a bevel gear pair. The tool 18 is arranged such that an upperline or generatrix 21 of a pitch cone 27 of the workpiece 1a extends asnearly perpendicular as possible to the axis 12 in the machining region.For the sake of simplicity, the workpiece 1a and the tool 18 are shownin FIG. 3 in composite section taken along the lines I--I for theworkpiece 1a and II--II for the tool 18.

FIG. 3 illustrates the axially displaced geometry of the tool 18relative to the workpiece 1a on the basis of a planar conjugate geargeometry well-known in the art and also in connection with matingrelationships of the graphic developments of the pitch surface of aplanar conjugate gear 30 associated with the crown gear 1 and the tool18. FIG. 3 also shows the workpiece 1a and the tool 18 in section andtheir respective pitch cones 27 and 26 in three projected views 47, 48and 49. The mating relationship and a section 40 through a tooth of thetool 18 are supplementarily illustrated on an enlarged scale in FIG. 4.A common reference point 23 is situated on a common longitudinal toothflank line 38 of the tool 18 and the planar conjugate gear 30. A planarconjugate gear center point 31 is connected with a cutting tool centerpoint 33 by a straight line 32. A pitch cone apex 34 of the tool 18 issituated on this straight line 32. A center of curvature 35 is situatedon a line 36 normal to a line 37 tangent to the common longitudinaltooth flank line 38 and at the reference point 23. A helix angle β_(R)and a helix angle β₁₈ of the planar conjugate gear 30 or the workpiece1a and of the tool 18, respectively, are each defined by the tangentline 37. An axis displacement angle φ is determined by the differencebetween the helix angle β₁₈ and ⊕_(R) and may be, for instance, 20°. Ascan be seen, there is good mating or matching between both graphicdevelopments of the pitch surfaces of the planar conjugate gear 30 andof the tool 18.

The crown gear 1 is shown in section in the projected view 48 projectedfrom a central conjugate radius 24 in FIG. 3. It will be seen that theconjugate gear center point 31 and the pitch cone center point 7 of thecrown gear 1 as well as the conjugate radius 24 and a line or generatrixof the pitch cone 27 all coincide. In turn, a projection of the pitchcone center point 34 is situated on this line. The position of the crowngear axis 3 is thus determined. The position of the tool axis 16 isdetermined by the pitch cone center point 34 and an intersection point28 with a line or cathetus 29, as will be most readily appreciated fromthe projected view 47. This location of the two axes 3 and 16 and thusof the workpiece 1a and the tool 18 corresponds to that shown in FIG. 2.

The projected view 47 makes clear the graphical determination of thepitch cone 26 and of a pitch circle 25 of the tool 18 which is designedas a hypothetical gear conjugate to the crown gear 1, preferably with askew angle hypoid geometry and with an abrading surface 19 on the toothflanks 20 of the helically conical toothing according to thisillustrative embodiment.

The position of both the pitch cones 26 and 27 relative to one anothercan be most readily seen from the projected view 49. The reference point23 is situated both upon a pitch circle 22 of the crown gear 1 as wellas on the pitch circle 25 of the tool 18. The tool axis 16 and the lineor cathetus 29 are mere projections. The pitch cone 27, the pitch circle22 and an angle δ are equivalent to those shown in the projected view48.

The hypoid geometry, in this illustrative embodiment a skew angle hypoidgeometry, of the tool 18 relative to the workpiece 1a is especially wellillustrated by the position of the crown gear axis 3 and the tool axis16 in the views of FIG. 3.

According to FIG. 5, it is now the rough machined pinion gear 2 which ismounted on the rotatable spindle 11 of the headstock 10 as a workpiece2a to be ground. The apex 7 of the pitch cone of the pinion gear 2 issituated on the axis 12 of the generating drum 13. A further tool 41having a further tool axis 42 is fastened to the spindle 17 of thepivoting component 15 and is also helically conical and provided withabrading tooth flanks 43 and is designed and arranged in FIG. 5 suchthat it also forms conjointly with the finish ground pinion gear 2 apreferably skew angle hypoid gear transmission. The pinion gear axis 4of the workpiece 2a extends in this illustrative embodimentsubstantially perpendicular to the axis 12, that is to the crown gearaxis 3 of the hypotheticcal associated crown gear 1 which is arranged onthe axis 12 of the generating drum 13 as a generating conjugate gear andwhich is represented by the pitch cone 27 and the pitch circle 22.

In FIG. 6, a tooth sliding diagram, which is equivalent to a grindingdirection diagram, is represented upon a segment of toothing of aworkpiece 1a or 2a. Due to the axial displacement, i.e. the displacementof the tool axis 16 or 42 relative to the workpiece axis 3 or 4,respectively, when the gears are in mesh a longitudinal relative slidingL between tooth flanks results along the tooth flanks in addition to theradial tooth sliding H. The magnitude and direction of a resultantvector representing the sliding R can be determined from the diagram.These values of magnitude and direction vary over the width of the toothand over the height of the tooth.

In FIG. 7, a tool tooth 50 is shown in section, corresponding to thesection 40 of FIG. 4, i.e. associated with the tool 18. Both tool flanks51 and 52 comprise a surface of abrading material 53, e.g. a coating orlamination 0.1 mm. thick of diamond powder or of Borazon, which isexcellently well suited as a grinding medium coating. The tooth toplands and tooth bottom lands can optionally also be coated.

Segments of the toothing of the workpiece 1a and the tool 18 are shownin FIGS. 8a, 8b and 9. According to FIG. 8a, for instance, all concavetooth flanks 55 are ground in a first machining operation and, accordingto FIG. 8b, all convex tooth flanks 56 of the toothing of the workpiece1a are ground in a second machining operation, for instance in that thetooth thickness of the tool 18 is designed less than the width of thecorresponding tooth gap of the workpiece 1a. There is then an air gapbetween the tooth flanks not currently being ground. Preferably,however, both the concave tooth flanks 55 and the convex tooth flanks 56are continuously ground in a single operation by the tooth flanks 51 and52 of the tool 18 provided with the abrading material 53 according toFIG. 9. Furthermore, tooth top lands 54 of the toothing can alsosupplementarily be provided with abrading material 53, so that inparticular the root or base fillet radii can also be conjointly ground.

A resultant velocity V_(R), in this illustrative embodiment the surfacespeed for grinding, is graphically determined in FIG. 10 on the basis ofplanar conjugate gear geometry well-known in the art and of thefollowing values:

Reference point 60, tool axis 61, mean conjugate radius 62, tool helixangle β₁, workpiece helix angle β₂, tool peripheral speed V_(U1),workpiece peripheral speed V_(U2) and normal velocity Vn.

The method according to FIGS. 1 through 10 functions as follows:

As is well known, bevel gear sets or bevel gear pairs with or withoutaxial displacement may be fabricated, for example, according to one oftwo well known bases of generation, i.e. the planar conjugate gearmethod or the generating mating gear method. Hypoid gear transmissionsfabricated according to planar conjugate gear geometry becomeincreasingly inaccurate as the relative displacement of the axes becomesgreater. Correct prerequisites for hypoid gear transmission, however,prevail again if the one gear is machined by plunge cutting only and theother gear according to generating mating gear geometry. In addition tothe tooth height sliding, longitudinal tooth sliding along the toothflanks according to FIG. 6 results, for instance, from the displacementof axes, for instance of a pinion axis relative to a crown gear axis.The magnitude and direction of the resultant R as a resultant slidingvelocity is thus capable of being influenced by the angle of axisdisplacement. This relative sliding velocity R is exploited according tothe invention as a surface speed V_(R) for finish grinding. A requisitecrown gear speed of rotation n₂ for a given grinding surface speed V_(R)will be determined on the basis of the following calculation example inconnection with FIG. 10. Given the following data:

nominal surface speed for grinding: V_(R) =15 m/s

average crown gear diameter: d₂ =150 mm

helix angle of crown gear: β₂ =25°

helix angle of tool: β₁ =60°

Then the crown gear speed of rotation n₂ is established andcalculatively determined according to the following well-known formulae:##EQU1##

This means that each tooth is ground approximately 28 times per second.If a magnitude of material removal of 0.001 mm is employed, then a flankgrinding rate of 0.028 mm per second results on all teeth. With agrinding allowance of approximately 0.2 mm a crown gear can therefore beground after hardening in less than one minute according to thisexample. The prerequisites for economical grinding are thus fulfilled.

For grinding the crown gear 1 according to FIG. 2 it is thus necessaryto design the grinding gear or rotary form tool as a conjugate gear suchthat both conjointly form a hypoid gear transmission. The crown gear 1and the tool 18 mesh in the ratio of their tooth numbers. The requisiterotational speed of the crown gear 1 is determined according to theabove example. The workpiece 1a and the tool 18 may be, for instance,driven in synchronism by two drive motors which are interconnected by aso-called "electric shaft", i.e. the spindles 11 and 17 are constrainedto rotate at predetermined rotary speeds in mutual synchronism.

The inventive apparatus will be described in more detail in relation tothe FIGS. 11 through 19. For grinding the toothing of the workpiece 1a,the feed motion of the tool 18 is effected in the direction of the axis12 of the generating or roll cradle 14, i.e. substantially perpendicularto the reference point 23. Both tooth flanks of the teeth are preferablycontinuously ground in a single grinding operation, since the workpiece1a and the tool 18 are in mesh.

Since in this case not generating motion is performed, the grindingprocedure can also be performed on a machine devoid of a generatingmechanism. As can be seen from FIG. 4, uncrowned longitudinal toothflanks are produced on the workpiece 1a in relation to the correspondingtooth flanks of the tool 18. The normally desired relative crowningbetween the pinion gear 2 and the crown gear 1 must therefore becorrespondingly provided when fabricating the tools 18 and 41. It isfurthermore also possible to provide that the rough machined toothing bedesigned such that not the entire tooth flank surface, but only amagnified contact pressure region be ground. As can be seen from FIG. 9,the tooth cross-section of the tool 18 does not correspond to the toothgap form of the workpiece 1a, since between the workpiece 1a and thetool 18 not only longitudinal motions but also height motions ensuingfrom machine engagement corresponding to FIG. 6 are performed.

The direction of rotation is selectively determined, preferably howeverin the direction indicated in FIG. 4, in order that the tool 18penetrate the workpiece 1a from the interior towards the exterior. Thiscontinuous grinding process not only eliminates the hardeningdistortion, but also axial run-out errors and radial run-out errors. Inparticular, pitch deviations can also be eliminated in that each toothof the tool 18 runs through each tooth gap of the workpiece 1a in anequalizing manner.

Grinding with an integral generating motion is represented in FIG. 5.The procedure is analogous to that of grinding the crown gear 1according to FIG. 2 except that a generating motion is now performed inknown manner about the generating axis 12 either as a supplementary oras an exclusive feed motion. By correspondingly designing the toothprofile on the tool, however, the necessity of performing a generatingfeed motion during grinding of generated bevel gears can becircumvented.

A rotary form tool for performing the inventive method is preferablydesigned such that, in addition to its hypoidal geometry, eachengagement surface of a tooth of the tool forms the negative of a toothgap of the finish ground workpiece in the ground region during grinding.Not necessarily but advantageously, the tool will comprise a skew angleddisplacement of its axis relative to the axis of the workpiece and willnormally differ from the axial relations of the bevel gear transmissionto be machined. It will furthermore comprise at least on one of itstooth flanks, either on a convex tooth flank or on a concave toothflank, a coating of grinding or abrading medium which can be renewed atwill. Preferably, however, all tooth flanks are thus coated and the toolexhibits a greater tooth length than the workpiece.

A tool may be, for instance, fabricated as follows:

a master gear of a bevel gear or hypoid gear transmission is coated onits tooth flanks with a grinding medium;

according to one method of the invention, a rough machined tool isground as a workpiece by the coated master gear as a tool; and

subsequently the rough machined and finish ground tool now constitutinga so-called "master negative gear" is in turn coated with a grindingmedium.

The master gear is preferably supplementarily coated with abradingmaterial in its bottom land regions in order that the top land regionsof the tool may be designed for grinding the base fillet radii, cf. e.g.the crown gear 1 in FIG. 9 with a tooth gap bottom land region 57 andthe tool 18 with the tooth top land 54.

On the other hand, corresponding data programs can, for instance, begenerated from a stored master gear set data program and therewithassociated machine setting data can be established for the tools and, ifnecessary, corrected until the generated bevel gears produce exactreplications of the master gears.

Turning now specifically to FIG. 11 of the drawings, the apparatusillustrated therein by way of example and not limitation and employed torealize the method as hereinbefore will be seen to comprise a machinebed 110. A first slide or carriage 111 translatable in the horizontaldirection in the drawing and a second carriage or slide 112 verticallytranslatable in the drawing are situated on this machine bed 110. Afirst spindle 113 driven by an electric motor 141 serves for translatingthe first slide 111 and a second spindle 114 also driven by an electricmotor 143 serves for translating the second slide 112. A rotary table115 with a housing 116 for journalling a first spindle 117 is fastenedto the first slide 111 and a rotary table 118 with a turret 139 (cf.FIGS. 14 and 18) is fastened to the second slide. A housing 119 forjournalling a spindle 120 is translatably guided on the turret 139. Thespindle 117 is driven by a first electric motor 121 and the spindle 120is driven by a second electric motor 122. The workpiece 127 through 130(see FIGS. 11 to 14) to be ground is fastened to the spindle 117 and atool 131 and 134 is fastened to the spindle 120 in a manner analogous tothe previously described tools 18 and 41.

Two rails or guideways 123 upon which the slide 111 is translatablyjournalled by means of guide members 124 are fastened to the machine bed110 according to FIG. 15. The rotary table 115 is rotatably journalledon this slide 111. Only an annular slot 125 of this journalling and twoof in total six clamping cups 126 with which the rotary table 115 can beclamped in any desired position on the annular slot 125 of the slide 111are visible in FIG. 15. The spindle housing 116 in which the spindle 117is journalled is fastened on the rotary table 115. The left half of thedrawing shows a spindle 117 of increased diameter for large workpieces127 and 129 (cf. FIGS. 11 and 13) and the right half of the drawingshows a spindle 117 of lesser diameter for small workpieces 128 and 130(cf. FIGS. 12 and 14).

The slide 111 is translatably guided on rails or guideways 123 of themachine bed 110 not particularly shown in FIG. 16 by means of the guidemembers 124 and with the aid of the spindle 113. The rotary table 115 isrotatably journalled on the slide 111. A worm wheel or worm gear 135which meshes with a worm 136 is fastened to the underside of the rotarytable 115. In order to rotate the rotary table 115 on the slide 111, theworm gear 135 is driven by an electric motor 137 (cf. FIG. 17) throughthe worm 136. In order that the rotary table 115 be easily rotatableupon the slide 111, a ball bearing 138 is provided in the middle of therotary table 115. For clamping the rotary table 115 in the desiredposition on the slide 111, the annular slot 125 is situated in the slide111 and a number of, for instance six, clamping cups 126 are arranged onthe rotary table 115 with the aid of which the rotary table 115 can beclamped to the annular slot 125 of the slide 111. The spindle 117 isjournalled in the usual manner in the spindle housing 116.

A turret 139 is fastened to the rotary table 118 according to FIG. 18.This turret 139 comprises two vertical rails or guideways 140 upon whichthe housing 119 is translatably journalled with the aid of guide members142. The spindle 120 is rotatably journalled in the housing 119 in theusual manner. The housing 119 of the spindle 120 on the rotary table 118is thus vertically translatably journalled on a turret 139 incontradistinction to the housing 116 of the spindle 117 which is fixedlymounted on the rotary table 115.

Both electric motors 121 and 122 are interconnected by a so-called"electric shaft" known per se and also known as an electronictransmission according to FIG. 19. This so-called "electric shaft" isnecessary since it is not possible to connect the tool and the workpiecewith one another through a mechanical transmission since the requisitespeed of rotation for grinding the workpiece is much too high and cannotbe transmitted by a gear transmission or the like from tool toworkpiece. At high speeds of rotation the wear of such a mechanicaltransmission would be excessive.

This so-called "electric shaft" comprises, according to FIG. 19, arotary speed regulator 144, a tacho-generator 145 and a pulse transducer146 for each electric motor 121 and 122. Both electric motors 121 and122 are driven in mutual synchronism at the desired speed of rotation byan electronic control 147. Since tool and workpiece are designed asgears, the speeds of rotation of both electric motors 121 and 122 mustbe proportional to the numbers of teeth of these gears. The electroniccontrol 147 is constructed in known manner and comprises an operatingconsole with a visual display unit and function buttons, a NC-system, anelectronic transmission, a module with inputs and outputs to thegrinding machine, et cetera.

One motor of the electric motors 121 and 122 is designed as a mastermotor and the other motor as a slave or servo motor.

The master motor should rotate faster than the slave motor, since theso-called "electric shaft" operates more precisely when the master motorrotates faster than the slave motor. The master motor should, however,preferably drive the tool and not the workpiece. Should it be requiredto grind the crown gear 1, then both conditions can be fulfilled, sincethen the pinion gear 2 serving as the tool 18 rotates more rapidly.However, should it be required to grind the pinion gear 2, then only oneof the two conditions can be fulfilled. Preferably the more rapidlyrotating workpiece 1a or 2a, namely the pinion gear 2, will be driven bythe master motor.

The grinding machine is therefore preferably designed according to FIGS.13 and 14 and the electric motor 122 on the turret 139 is employed asthe master motor 122 and the electric motor 121 is employed as the slavemotor 121 and also as the spindle 120 for accommodating thepredominantly more rapidly rotating pinion, whether tool or workpiece.

The so-called "electric shaft" can be digital-controlled oranalog-controlled. Digital control is preferably employed for thisgrinding machine. When digitally controlled, the master motor, forinstance the electric motor 122, generates pulses during its rotationwhich are exploited for controlling the slave motor, for instance theelectric motor 121. For each pulse emitted by the pulse transducer 146,the master motor 122 rotates through an angle α₁ and causes the slavemotor 122 to rotate through a related angle α₂. The followingrelationships obtain: ##EQU2## wherein: Z₁ =number of teeth of the geardriven by the master motor 122;

Z₂ =number of teeth driven by the slave motor 121;

α_(act) =actual angular displacement of the master motor 122; and

α_(ref) =reference angular displacement for the slave motor 121.

In this controller, it is essential that a tooth of the workpiece or ofthe tool be situated in a predetermined position, for example exactly inthe middle of a tooth gap of the conjugate gear. If the tool and theworkpiece are brought into mesh, one tooth of the tool must therefore becorrespondingly positioned, for instance in a tooth gap of theworkpiece, for instance must be centered therein. There are variousprocedures for this positioning or centering which can be performed withor without a digitally controlled so-called "electric shaft".Procedures, preferably for centering, will be described in detail in thefollowing in relation to FIGS. 13 and 19. Before the actual positioningor centering, the tool and the workpiece must be brought into positionsuch that tooth can no longer encounter tooth. It is furtherprerequisite that the control means for this procedure be predominantlyintegrated in the controller 147.

According to a first illustrative embodiment, centering is performedwith stationarily meshed gears. The pulse transducer 146, which is alsodesignated as an incremental rotational stepper transducer, is employedas a contact transducer of the master motor 122. Such a pulse transducerhas a high resolution of, for instance, one pulse per 1/1000 of a degreeof rotation. The slave motor 121 is rotated until both gears touch, i.e.until their tooth flanks enter into contact, when the pulse transducer146 of the master motor 122 transmits a pulse to the controller 147.Thereupon the slave motor 121 is rotated in the opposite direction untilthe gears touch once again, i.e. until their opposite tooth flanks enterinto contact, and the pulse transducer 146 of the master motor 122transmits another pulse. Subsequently, the direction of rotation of theslave motor 121 is reversed again and the slave motor 121 is rotated bya half of the previous amount so that a tooth of one gear is situatedexactly in the middle of a tooth gap of the other gear. Should thepredeterminate definitive position be, for instance, situated notexactly in the middle, the slave motor 121 is positioned by acorrespondingly different amount.

According to a second illustrative embodiment, centering is performedwith rotating meshed gears. As long as both gears rotate withouttouching, i.e. with bilateral play between their tooth flanks, the lagbetween the master motor 122 and the slave motor 121 will be relativelysmall. It will be understood that the lag is the difference between thereference value for and the actual value of the position of the slavemotor 121. As soon as both gears touch, however, this lag is altered,since the slave motor 121 only delivers the torque necessary forrotating its associated gear alone. The alteration of the lag isevaluated in the controller or controller circuit 147 for centering atooth of one gear in the tooth gap of the other gear analogous to theabove-described illustrative embodiment.

According to a third illustrative embodiment, centering is alsoperformed with rotating meshed gears. The contact of both gears isrecognized by a microphone. The impact of one tooth flank on theadjacent tooth flank generates acoustic waves which can be evaluated forcentering the gears in the described manner.

According to a fourth illustrative embodiment, the workpiece 129 is notbraked. One of the teeth of the tool 133 connected to the master motor122 is inserted into a tooth gap of the workpiece 129. As soon as atooth flank of the tool 133 touches a tooth flank of the tooth gap ofthe workpiece 129, a torque is generated by this contact with theunbraked workpiece 129. This torque is measured by a torque transducer.This contact-generated torque, in turn, generates a pulse which causesthe master motor 122 and the tool 133 to begin to rotate until the othertooth flank of the tool touches the other flank of the tooth gap of theworkpiece. During this rotation, the master motor 122 or the slave motor121 generates in the pulse transducer 146 a further number of pulseswhich are counted. As soon as the other flank of the tooth of the tool132 touches the other flank of the tooth gap of the workpiece 129, acounteracting torque is generated and the master motor 122 is reversedin its direction of rotation and rotated back by half of the countedpulses. Thus one tooth of the tool is situated exactly in the middle ofa gap of the workpiece.

The behavior of a so-called "electric shaft", i.e. of an electronictransmission, is considered to be well-known in the art. The associatedregulation technology can be refined to the extent desired, so that therequisite coincidence of the angular displacement of the tool shaft andthe workpiece shaft is attainable, especially since when grinding, i.e.finish machining bevel gears considerably smaller force fluctuationsarise than when cutting, i.e. rough machining bevel gears. Since theslave motor 121--which is incrementally driven by the master motor 122through the electronic controller 147--must set a relatively great massinto motion, namely the shaft and the gear, oscillations of this massare inevitable. These oscillations are, however, largely damped by thegrinding process and can even have beneficial effects.

The regulation technology usual in "electric shafts" can be improved inthat, for instance, a supplementary adaptive regulator is employedhaving a variable amplification of the rotary speed function.Additionally, a so-called "observer regulator" can be employed ifregulating algorithms are implemented.

The mode of operation of the grinding apparatus will now be explained inrelation to FIG. 13:

First the workpiece 129 is mounted on the spindle 117 and the tool 133is mounted on the spindle 120. Subsequently, a tooth of the tool 133 ispositioned for centered in a tooth gap of the workpiece 129 in one ofthe manners described hereinbefore and the master motor 122 and theslave motor 121 are allowed to run free at full speed, the tool 133 andthe workpiece 129 having been so arranged in relation to one anotherthat their teeth do not touch during the acceleration of the tool 133and the workpiece 129 to their fully rotary speeds. This is essential,since in the acceleration phase an undesirably great lag between themaster motor 122 and the slave motor 121 can arise. Only when the fullrotary speeds of the master motor 122 and of the slave motor 121 havebeen attained are the tool 133 and the workpiece 129 advanced into thegrinding or finish machining position. The workpiece 129 is now groundor abraded, i.e. finish machined, at full rotary speed with apredetermined feed motion. Before the rotary speeds of both motors 121and 122 are subsequently reduced, the tool 133 and the workpiece 129 arepreferably disengaged from mesh. This is also essential, since anundesirably great lag can also arise in the deceleration phase.

While there are shown and described present preferred embodiments of theinvention, it is to be distinctly understood that the invention is notlimited thereto, but may be otherwise variously embodied and practicedwithin the scope of the following claims. ACCORDINGLY,

What we claim is:
 1. An apparatus for finish machining tooth flanks of anumber of longitudinally curved teeth of a rough machined bevel gearblank for a hypoid bevel gear pair, comprising a ring gear and a piniongear, by means of a rotary form tool, comprising:a machine bed; twoslides arranged on said machine bed to be translatable toward oneanother; a first spindle having a lengthwise axis and serving formounting the rough machined bevel gear blank defining a workpiecearranged on one of said two slides; a second spindle having a lengthwiseaxis and serving for mounting the rotary form tool and arranged on theother of said two slides; said slides constituting means fortranslatably adjusting said first spindle and said second spindle; aseparate electric motor arranged coaxially with respect to each of saidtwo spindles for respectively driving the rotary form tool and theworkpiece at a first and a second speed of rotation, respectively; meansdefining an electric shaft; said separate electric motors being mutuallyinterconnected by said electric shaft, for synchronizing said first andsaid second speed of rotation in a predetermined ratio; said slides eachcomprising a rotary table with a housing for journalling a respectiveone of said two spindles and a therewith associated one of said separateelectric motors; said rotary tables each having an axis of rotation; atleast one housing of said housings being mounted on one of said rotarytables to be translatable in relation to said axis of rotation of theassociated rotary table; said rotary tables each being rotatable suchthat there can be selectively adjusted the angle between the lengthwiseaxes of the first and second spindles; one of said spindles beingarranged such that the lengthwise axis thereof intersects the axis ofrotation of the associated rotary table; and the other of said spindlesbeing arranged such that the lengthwise axis thereof is arranged offsetwith respect to the axis of rotation of the associated rotary table. 2.The apparatus as defined in claim 1, wherein:one motor of said separateelectric motors is arranged in said at least one housing which istranslatable; said one motor being structured as a motor motor; oneother motor of said separate electric motors being arranged in one otherof said housings; said one other motor being structured as a slavemotor; one spindle of said two spindles being driven by said mastermotor; and said one spindle normally carrying the pinion gearselectively constituted by the workpiece or the rotary form tool.